A mobile phone of the aforementioned type is known. The mobile phone includes a streaming server generally compatible with the UPnP (Universal Plug and Play) network protocol, or respectively with the DLNA (Digital Living Network Alliance) interoperability standard, the server then being called a UPnP server or DLNA server, respectively. Such a server makes it possible to stream media saved in an internal memory of the phone to a remote client equipment also compatible with the UPnP network protocol, or with the DLNA standard. The streamed media includes audio and/or video data. The mobile phone also includes a means for converting the file stored in the internal memory, such as a transcoding application when the format of the media saved in the memory, and intended to be streamed toward the remote client equipment, is not compatible with the formats supported by the remote client equipment.